Dear Aspirant,

Mechanical Engineering is the best option to choose to get into ISRO. It comprises all the field of design, manufacturing, & Engine structures. Electrical engineering is also good field to choose to get into ISRO
In mechanical engineering, you have much more job opportunities but since it is one of the widely selected field, there is a really high competition. Mechanical engineering has one more advantage, there are more institutes providing mechanical engineering degree than aerospace engineering .

Aerospace engineers and mechanical engineers both work on the development and construction of equipment and devices. The major difference between these two are that the former is relatively narrow field  focusing on airplanes and other aerospace related machines. by contrast mechanical engineering is a broad field that encompasses work in a wide variety of industries and serving a multitude of purposes. Aerospace engineers tackles aerodynamics and flight mechanics in a way that mechanical engineer typically do not. Now coming to the career options after completing B Tech in mechanical engineering and aerospace engineering. Well aerospace engineers are highly paid professions in the engineering job market. However in recent years the availability of aerospace engineers increased drastically. Key areas of employment after completing aerospace engineering are are in space research centres like NASA and ISRO, aeronautical development establishment, aeronautical laboratories, aircraft manufacturing companies, defence research and development organisation, defence services, department of Civil aviation etc. in case of mechanical Engineering jobs directly related to your degree include automobile engineering contracting civil engineering control and instrumentation Engineering etc.

But nowadays demand of Mechanical Engineering in market has drastically decreased and the median salary it is also not up to the mark. Now the choice is yours if you you can pursue mechanical engineering from an well-established institute is obviously a good choice.
Hope you have understood.